# Metric Math Conversion Problems

In these lessons, we will look into some methods that can be used for metric conversion problems. The first method uses the metric table and can also be regarded as a shortcut method. The second method uses the metric staircase and the third method uses the unit fraction method.

The following diagrams show some metric conversions for lengths and weights. Scroll down the page for examples and solutions.

Metric Conversion Methods
Shortcut Method Metric Staircase Unit Fraction

### Convert using a Metric Table or Shortcut Method

The metric system uses prefixes to denote multiple of 10.

The following table shows some common prefixes of metric units and how to convert between them.

Each prefix differs by a multiple of 10 from the next prefix. When converting between the different units of measure, we look at the number of “jumps” between the prefixes of the two units and then multiply or divide by the powers of 10 accordingly (moving to the right would mean to multiply and moving to the left would mean to divide).

Example:
Convert 3 km to m

Solution:
There are 3 “jumps” to the right from kilometer to meter.

So, we multiply by 103 = 1000

3 km = 3 × 1,000 = 3,000 m

Example:
Convert 20 mm to cm

Solution:
There is 1 “jump” to the left from millimeter to centimeter

So, we divide by 10.

20 mm = 20 ÷ 10 = 2 cm

How to convert to different metric units of measure for length, capacity, and mass?
The metric system is widely used because it is based on the powers of 10. This allows for easy conversion between smaller and larger units.
The basic unit of length is the meter(m). It is just over 1 yard.
The basic unit of weight is the gram(g). One gram is the mass of 1 cubic centimeter of water.
The basic unit of capacity or volume is liter(l). A liter equals 1000 cubic centimeters.
Examples:
Complete each conversion

1. 6.3km = ____ m
2. 62,300cm = ___ hm
3. 37,200g = ___ kg
4. 1.73hg = ___ dg
5. 93.7L = ___ mL
6. 62,300cL = ___ kL

How to perform metric conversion using the table or shortcut method?

Use the mnemonic “King Henry Drinks Ucky Dark Chocolate Milk”

Examples:

1. 0.521 mm to m
2. 9501 g to kg
3. 40.6 L to mL
4. 1457 dm to hm
5. 53.45 dag to mg
.4 kL to mL

How to convert metric units of weight without using a calculator?
The presentation focuses on conversion between kg, g, and mg.
Imagine a 1 kilogram(kg) tablet which is made up of a 1000 smaller gram(g) tablets which is in turn made up of 1000 even smaller milligram (mg) tablets.
Big to small: multiply
Small to big: divide

How to multiply and divide by 1000 in conversion of metric units?
This tutorial explains answers to exercises in converting metric units of weight. The exercises involve multiplying and dividing without a calculator.

### Metric Staircase or Ladder Method

How to use the metric staircase to convert units within the metric system?
Another method similar to the table method is to use the metric staircase. It is also called the ladder method.

Use the mnemonic “Kangaroo Helps Dingo Because Dingo Can’t Multiply”

How to use the metric staircase to convert between metric measurements?
When you go up the stairs to the left, move the decimal to the left.
When you go down the stairs to the right, move the decimal to the right.

### Convert using the Unit Fraction Method

In this method, we multiply by a unit fraction in order to perform the metric conversion.

Example:
Convert 3 km to m

Solution:

Example:
Convert 20 mm to cm

Solution:

Common Metric Length Conversions Using Unit Fractions

Common Metric Weight Conversions Using Unit Fractions

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.